Question

Calculation of Body Mass Index A biochemistry professor weighs \(260 \mathrm{lb}(118 \mathrm{~kg})\) and is 5 feet 8 inches \((173 \mathrm{~cm})\) tall. What is his body mass index (BMI)? How much weight would he have to lose to bring his BMI down to 25 (normal)?

Short answer

Current BMI: 39.4. Needs to lose about 43.18 kg to reach a BMI of 25.

Step-by-step solution

Understanding BMI Formula

The formula to calculate Body Mass Index (BMI) is: \[ BMI = \frac{\text{weight in kg}}{(\text{height in meters})^2} \] We'll use this formula to calculate the professor's current BMI.

Convert Height to Meters

First, convert a height of 173 centimeters to meters. Since 1 meter equals 100 centimeters, we have: \[ \text{Height in meters} = \frac{173}{100} = 1.73 \text{ meters} \]

Calculate Current BMI

Substitute the professor's weight and height into the BMI formula: \[ BMI = \frac{118}{(1.73)^2} \] Compute the value: \[ BMI \approx \frac{118}{2.9929} \approx 39.4 \] This is the professor's current BMI.

Calculate Desired Weight for BMI 25

To find the weight for a BMI of 25, set the formula to 25 and solve for weight: \[ 25 = \frac{\text{weight in kg}}{(1.73)^2} \] Solving for weight: \[ \text{weight in kg} = 25 \times (1.73)^2 = 25 \times 2.9929 \approx 74.82 \text{ kg} \] Therefore, the professor's target weight for a BMI of 25 is approximately 74.82 kg.

Calculate Weight Loss

Calculate how much weight the professor needs to lose to reach the target weight:\[ \text{Weight Loss} = 118 \text{ kg} - 74.82 \text{ kg} \approx 43.18 \text{ kg} \] Hence, the professor needs to lose about 43.18 kg to achieve a BMI of 25.

Key concepts

Weight Conversion

Weight conversion is a process of changing weight from one measurement system to another. In this context, we often deal with converting pounds (lb) to kilograms (kg), since the BMI formula uses weight in kilograms. 1 pound is approximately equal to 0.453592 kilograms, and to convert pounds to kilograms, you can multiply the number of pounds by this conversion factor. For example, if someone weighs 260 pounds, you can convert this to kilograms by multiplying:

• 260 lb × 0.453592 kg/lb ≈ 118 kg.

This conversion is essential because the BMI formula requires weight in kilograms for accurate calculation.

Height Conversion

Height conversion is often necessary in BMI calculations, especially when height is given in feet and inches, but the BMI formula requires height in meters. To convert height from feet and inches to meters, first convert feet to inches (since there are 12 inches in a foot), then add any additional inches. Next, convert the total height in inches to centimeters. Finally, convert centimeters to meters, as there are 100 centimeters in a meter. For example, a height of 5 feet 8 inches can be converted as follows:

• 5 feet × 12 inches/foot = 60 inches
• Total inches = 60 + 8 = 68 inches
• 68 inches × 2.54 cm/inch = 172.72 cm
• 172.72 cm / 100 = 1.7272 meters

Always ensure to round appropriately based on the required precision for your calculations.

Normal Body Mass Index

A normal Body Mass Index (BMI) typically ranges between 18.5 and 24.9. This range is interpreted as a 'healthy' weight status for most adults. The BMI provides a simple numeric measure of a person's body fat or thinness, relative to their height and weight. It is crucial to remember that BMI is a screening tool and not a diagnostic measure. Various health professionals might consider additional factors, like muscle mass, bone density, overall body composition, and individual assessment when interpreting BMI. But for general guidance, aiming for a BMI within the normal range is often recommended for reducing the risk of chronic diseases associated with overweight and obesity, such as diabetes, hypertension, and heart disease. In our exercise, the professor is advised to aim for a BMI of 25, which is at the upper limit of the normal range.

Weight Loss Calculation

To calculate necessary weight loss to achieve a specific BMI, it is important to first find the desired weight associated with the target BMI. This involves rearranging the BMI formula to solve for weight. Starting with the formula:\[ BMI = \frac{\text{weight in kg}}{(\text{height in meters})^2} \]We can rearrange it to solve for the target weight:\[ \text{Weight in kg} = \text{BMI target} \times (\text{height in meters})^2 \]For example, to reach a BMI of 25, we calculate:

• 25 × (1.73 meters)^2 ≈ 25 × 2.9929 ≈ 74.82 kg

Finally, subtract the target weight from the current weight to find the required weight loss. For the professor, it is:

• 118 kg - 74.82 kg ≈ 43.18 kg

Therefore, the professor would need to lose approximately 43.18 kg to reach a BMI of 25, which is considered the higher boundary of a normal BMI range.